Convergence and inequality in the world. The neoclassical or the AK model?

Advanced macroeconomics

Dr hab. Joanna Siwińska-Gorzelak

During the last lectures…

• ... we derived a model that has the „AK” structure, which highlights the importance of government spending & taxes

• This model (or rather – this structure of the model) is not unusual – the Ak models are quite simple to "create" – one needs to introduce in to the Cobb-Douglas function a factor of production, that is a function of capital… For example, Romer (1986), in his famous „learning -by-doing „model, suggested (following Arrow) that: A = g (K), which if used together with Y = Kα (AN) 1-α… ... .results in AK model

Ak models

• Ak models constitute quite a large group

• The conclusions arising from them are interesting.

• They stress the importance of economic policy, savings, and a whole range of other determinants for long-term growth In its simplest form they provide for convergence

Ak models & neoclassical modes

• The existing growth models can be divided into several broad groups.

• Among them are :

– Models of neoclassical (Solow model for example)

– Ak models (models endogenous older generation)

• Both of these approaches are interesting. The question is:

• Which is closer to the truth?

• One of the tests may be the phenomenon of convergence

Convergence

• "The convergence hypothesis or the catch-up effect - poorer countries’ income per capita (measured by GDP / person) will grow faster than GDP per capita of the rich countries. According to this hypothesis, the relative backwardness can facilitate the economic development of the country; hence – can be an advantage .

• Such a situation is called a catch-up effect”

• https://www.nbportal.pl/slownik/pozycje-slownika/konwergencja

Convergence

• Note however, that the Solow model predicts CONDITIONAL convergence- poorer countries’ income per capita (measured by GDP / person) will grow faster than GDP per capita of the rich countries, provided that both the rich and poor countries have the same steady-state.

• There is no reason the expect ABSOLUTE convergence (i.e. that poor countries will grow faster than the rich countries); but – if the Solow model is correct – we should observe conditional convergence

Convergence

• In the literature on economic growth, there are two ways to measure convergence.

• The first (sometimes called "sigma-convergence") refers to a decrease in the dispersion in the GDP per capita (standard of living) between different societies.

• The second - called "beta-convergence„ occurs when poor countries grow faster than rich ones.

• Economists talk about "conditional beta-convergence," when the economy is experiencing "beta-convergence," but it depends on other conditions "

Convergence

• To repeat once more: we expect to observe sigma-convergence among similar countries (or regions) but not among different ones

• We also expect to observe conditional beta-convergence, even in a very large sample of different countries (as this kind of empirical test takes into account the differences across countries)

Convergence

• Absolute (unconditional) beta convergence (all γ = 0) & conditional beta convergence (full version of the equation below)

• Sigma convergence

tataz

n

z ztaa

ta

taxy

y

y,,,11,

,

,

tTt

Convergence

• Note that if there is „sigma” convergence, there is also „beta” convergence

• The other way around – no!

Convergence and divergence

Źródło: Sala-i-Martin,

Convergence – theoretical foundations

• Convergence stems from the assumption of declining marginal revenue of capital: the same amount of capital invested in a poor country, where capital is scarce, it will bring much greater benefit than in rich country (neoclassical models).

• Another reason: the ability of poor countries to use (low-cost) technologies already developed in the rich countries.

• In rich countries, they are outdated, but at the same time they can technically revolutionize production in poor countries.

• In addition to saving time and money for research in science and technology, these countries minimize the risk of failure of a given technology

Convergence – states in the USA

Źródło: Sala-i-Martin, 1996

Convergence – states in the USA

Źródło: Sala-i-Martin, 1996

Convergence – prefectures in Japan

Źródło: Sala-i-Martin, 1996

Convergence – regions in Europe

Źródło: Sala-i-Martin, 1996

Convergence

• Econometric research almost undoubtedly shows that conditional convergence exists

• The econometric research shows that there is a statistically significant relationship between GDP per capita and it’s growth rate, when one controls for the investment rate, the stock of human capital, international trade, financial depth, government spending, etc

According to IMF (and other researchers)

• Convergence has entered into a new phase…

• Since the 90’s the developing countries are growing much quicker that the rich countries

• This is explained by globalization forces, favorable demographic trends (slowdown in population growth plus the still young society), better quality of institutions (governance), the improvement of macro-economic stability, sectoral transformation, etc Will this trend continue?

Convergence in recent times

Źródło: Dervis, 2012

Convergence in recent times

• Rodrik, 2011

(Conditional) convergence at the country level

Rodrik, 2011

(Absolute) convergence at the industry level

Rodrik, 2011

Growth decomposition

Rodrik, 2011

Summary

• Poor countries do not automatically grow faster than the rich ones - there is no "sigma" convergence or absolute "beta" convergence among all countries of the world

• Conditional „beta” cconvergence is a fact (empirically identified in the overwhelming number of studies) - although the process is quite slow. Rodrik (2011) noted that there is unconditional convergence at the sectoral (industry) level = ("industries") - this means that the change of economic structure to towards highly productive sectors is crucial. This is relatively new & very interesting

BUT..

• Convergence is a concept related to income (in)equality. If countries are converging, than inequality should decrease

• In some countries the „within” country inequality is growing

• There are still countries which are not developing

• These issues belong to the more imporant contemporary problems

Poverty traps?

Poverty traps

Poverty traps

Branko Milanovic: 3 ways to think about inequality

Gini coefficient

• https://en.wikipedia.org/wiki/Gini_coefficient

Gini coefficient for the 3 concepts of inequality

Milanovic B., 2012

Inequality – world vs. countries

Milanovic B., 2012

Who gained, who didin’t - the (famous) Elephant

Milanovic B., 2012

The class or the country – what predicts your income?

Milanovic B., 2012

Within and between inequality

Milanovic B., 2012

Migrations – Branko Milanovic

Branko Milanovic

I used the following sources:

• Sala-i-Martin, The classical approach to convergence analysis, The Economic Journal, 1996

https://www.nes.ru/dataupload/files/science/reset/Sala_i_Martin1996ej.pdf

NBP, Portal Edukacji Ekonomicznej; hasło „Konwergencja” https://www.nbportal.pl/slownik/pozycje-slownika/konwergencja Milanovic Branko (2012) „Global Income inequality by the numbers” .

Policy Research WP https://www.gc.cuny.edu/CUNY_GC/media/CUNY-Graduate-

Center/PDF/Centers/LIS/Milanovic/papers/2013/gpol12032.pdf • Dervis, K. (2012) „Convergence, Interdependence, and Divergence”

Finance & Development, September 2012, Vol. 49, No. 3